3. Determine which input-output systems given below are (i) homogeneous, (ii) additive, and (iii

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3. Determine which input-output systems given below are (i) homogeneous, (ii) additive, and (iii) linear. (a) $y(t) = \int_0^t x(t - \tau)x(\tau)d\tau$ (b) $y(t) = 4t\frac{dx}{dt} - 2x(t)$ (c) $y(t) = (x^3(t) + x^3(t - 2))^{\frac{1}{3}}$ (d) $y(t) = e^{-t}x(t - 1)$